Multivariate Statistical Analysis for the Classification of Sausages Based on Physicochemical Attributes, Using Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS)

Sausage is a convenient food that is widely consumed in the world and in Vietnam. Due to the rapid development of this product, the authenticity of many famous brands has faded by the rise of adulteration. Therefore, in this study, principal component analysis (PCA) was combined with chemical analysis to identify 6 sausage brands. Sausage samples were dried and then ground to a fine powder for both instrumental analyses of attenuated total reflectance-Fourier transform infrared (ATR-FTIR) and inductively coupled plasma–mass spectrometry (ICP-MS). Dried measurements of ATR-FTIR was performed directly on the ZnSe crystal, while elemental data were obtained through microwave digestion before the ICP-MS analysis. Principal component analysis (PCA) within the framework software of XLSTAT and STATISTICA 12 was performed on the spectroscopy and elemental dataset of sausage samples. PCA visualized the distinction of 6 sausage brands on both datasets of ATR-FTIR and ICP-MS. The classification on the spectroscopy profile showed that although more than 90% variation of the dataset was explained on the first two PCs, the difference between several brands was not detected as the distribution of data overlapped with one another. The PCA observation of the elemental composition on PC1 and PC3 has separated the sausage brands into 6 distinctive groups. Besides, several key elements contributed to the brands' identification have been detected, and the most distinctive elements are Na, K, Ca, and Ba. PCA visualization showed the feasibility of the classification of sausage samples from different brands when combined with the results of FT-IR and ICP-MS methods. The experiment was able to differentiate the sausages from the 5 brands using multivariate statistics.


Introduction
Sausage is processed food with the main ingredients consisting of types of meat (pork, beef, and chicken), salt, herbs, and spices [1,2].According to data from Statista [3], the top market for meat and sausages in 2022 is the United States at the top (38,976.6 million USD), Germany second (33,611.68 million USD), and France at third (17,264.51 million USD).With many advantages of high nutrition and convenient usage, sausage is favored by Vietnamese consumers.According to WMS predictions, the compound annual growth rate of sausages and salami in Vietnam in the period 2020-2025 will reach 6.26% per year with a total market value estimated at 728.28 million USD by 2025 [4], and Vietnam already at number 23 (1,074.77 million USD) in 2022 [3].Tis trend shows that sausage has great potential for development, so it attracted huge investments from food companies.Currently, there are many types of sausages from big brands available on the domestic market such as Vissan, CP, Dabaco, and Duc Viet.However, due to the popularity of these products, leading to the low price, many fake, low-quality, unlabelled, and unclear origin products are rampant, posing a threat to consumers' health [4,5].Tese products can contain nitrosamine and polycyclic aromatic hydrocarbon compounds that are carcinogenic and can cause colorectal adenoma [6,7].Some studies reported microbial contamination during sausage processing [8][9][10][11].Although the samples were treated by heat, Staphylococcus aureus, Escherichia coli, and Lactobacillus viridescens were still detected, and some samples were beyond the limit for coliforms.To contribute to the quality control of sausages, grading measures are necessary.
Statistical methods have long been recognized as powerful tools in food classifcation and quality assessment [12].Some studies reported that the utilization of statistical methods in chemistry tends to increase over the years.Among them, the principal component analysis (PCA) and cluster analysis (CA) are the two most favorable tools [13][14][15].However, only statistical methods are insufcient for the assessment of the quality and identify food category; it is usually accompanied by the data obtained from measuring methods such as physicochemical property analysis (moisture, crude protein, ether-extractable fat, and ash) [16][17][18][19][20], meta-imaging spectra [21], microcomputing tomography [20,22,23], and chemical data (nutrient content and multielement content) [24,25].However, the determination of physicochemical properties in foods is time-consuming and complicated [16][17][18][19][20].In the case of the utilization of hyperspectral imaging, additional algorithms should be used to reduce the infuence of the distribution of meat and fat in the sausage [26].Tus, to simplify the classifcation, spectral data from FT-IR analysis and multielemental composition from the ICP-MS technique were employed to conduct the multivariate statistical analysis.
Many studies have demonstrated the feasibility of this combination.Nesakumar et al. applied the combination of PCA and FT-IR to determine the moisture content and age of beetroot, with the accuracy of the beetroot quality prediction model up to 97.5% [27].Yan Wang et al. [28] decided to combine PCA with ICP/MS/MS to explore each relationship between the content of 30 elements in rice and the production site.Based on the macronutrient content and cluster analysis, the samples were precisely divided into two main categories and six subcategories according to the place of production.Notably, there was a signifcant correlation between the elemental content in rice and the place of production, and thus, the origin of rice can be traced.In another study, the classifcation of pakchoi (Brassica rapa L. ssp.Chinensis) according to six growing regions using multivariate statistical methods (PCA) and ICP/MS has been applied successfully [29].
To the best of our knowledge, no studies that employed chemical analysis combined with multivariate statistics to identify sausages from diferent brands have been conducted.Terefore, in this paper, FT-IR and ICP-MS were the techniques combined with multivariate statistical methods to distinguish the brand names of sausage samples.
In the realm of food science and market dynamics, the necessity to distinguish between various sausage brands emerges from several pivotal concerns, paramount among which is the complexity and rapid expansion of the global and specifcally Vietnamese sausage markets.Tis burgeoning diversity, while ofering consumers a wide array of choices, concurrently engenders challenges in maintaining product authenticity and quality assurance.A critical aspect underpinning this study is the escalating incidence of adulteration within the market.Te proliferation of sausage brands has been accompanied by an alarming rise in products that are not only counterfeit or of inferior quality but also potentially hazardous to consumer health.Such products frequently contain harmful substances such as nitrosamines and polycyclic aromatic hydrocarbons and are prone to microbial contamination, including pathogens such as Staphylococcus aureus, Escherichia coli, and Lactobacillus viridescens.Tese adulterated products not only undermine the integrity of established brands but also pose signifcant public health risks.
Consequently, there is an imperative need for robust and efcient methodologies capable of authenticating sausage brands to safeguard consumer interests and health.Traditional methods for quality assessment and brand diferentiation in the sausage industry, while valuable, often fall short in terms of specifcity, efciency, and scalability.Tey are typically time-consuming, and labor-intensive, and may not provide the requisite resolution to distinguish between closely related or similarly formulated products.Addressing this lacuna, the present study introduces a novel approach that synergizes principal component analysis (PCA) with advanced chemical analysis techniques, namely, attenuated total refectance-Fourier transform infrared (ATR-FTIR) spectroscopy and inductively coupled plasma-mass spectroscopy (ICP-MS).Tis methodological fusion is designed to exploit the unique chemical fngerprints of sausage samples, thereby enabling a more nuanced and precise diferentiation of 2 Journal of Analytical Methods in Chemistry brands.Te PCA, in particular, ofers a powerful statistical tool to analyze complex datasets, reducing dimensionality and highlighting patterns and variations that are indicative of brand-specifc characteristics.Furthermore, the study's approach addresses the logistical and practical challenges associated with sausage quality control.By employing ATR-FTIR and ICP-MS, the research circumvents the limitations of more conventional physicochemical analysis methods.Tese advanced techniques allow for rapid, nondestructive analysis of the samples, providing a comprehensive profle of their chemical makeup, including both organic and inorganic constituents.Te integration of PCA serves to distill this voluminous data into actionable insights, efectively diferentiating between brands based on their distinct spectral and elemental signatures.
By establishing a reliable and efcient protocol for brand authentication, the research directly contributes to mitigating the risks associated with food adulteration.It provides a framework that can be adopted by regulatory bodies and manufacturers alike to ensure that the products reaching consumers are genuine, safe, and of the quality that they purport to be.In essence, this study not only addresses a specifc market need but also contributes to the broader discourse on food safety, consumer protection, and the integrity of food supply chains.

Method.
Operating parameters for ICP-MS measurement are shown in Table 1.Statistical analysis of the data was performed using XLSTAT (Lumivero, Denver, USA) and STATISTICA 12 (Dell Software, USA).Principal component analysis (PCA) was applied to analyze data obtained from FT-IR and ICP-MS analyses to evaluate the distinctions between sausage samples from 6 brands.Te outputs of the multivariate statistical analysis include a screening histogram to show the contribution of the principal components to the PCA model, a score scatter plot illustrating the separation of 6 diferent groups, a loading scatter plot explaining the infuence of factors on clustering, and the moving range graph illustrating the means and the general distribution of the variables across the cases [29].

Sample Preparation.
Sixty sausage samples were systematically obtained from six distinct brand names-Ebol, Lacus, Bucher, ÐN Á, Le Gourmet, and Vissan-with each brand contributing 10 samples.Tese samples were collected from various supermarkets in Hanoi to ensure geographical diversity and thereby maximize the robustness of the study's fndings.

Sample Preparation.
Each sausage sample, weighing approximately 50 grams, underwent a meticulous sample preparation procedure.Initially, the samples were minced and subsequently subjected to alcohol immersion for 15 minutes as a pretreatment step.Tis was followed by a drying process carried out at 70 °C for 24 hours.Postdrying, the samples were ground to a fne consistency utilizing a Seka SK200 grinder.To ensure uniformity and eliminate moisture, the ground samples were enveloped in oil-absorbent pads and subjected to further grinding using a mortar and pestle.Te homogenized samples were then stored at a temperature of 4 °C until further analysis.

Fourier Transform-Infrared (FT-IR) Spectroscopy
Analysis.Prior to FT-IR analysis, the ground samples were sifted using sieves with mesh sizes ranging between no. 100 and no.120, aimed at isolating particles with dimensions falling within the 0.125-0.150mm range.Tis sieving process minimized the potential impact of radiation scattering attributable to variable particle sizes, thus ensuring analytical consistency.Te FT-IR measurements were conducted using an ATR-FTIR instrument, covering a wavelength spectrum between 4000 and 400 cm^−1.Each sample was subjected to 128 scans with a spectral resolution of 4 cm^−1, and measurements were replicated six times to afrm the reliability of the data.

Elemental Analysis.
For the elemental composition determination, approximately 0.2 grams of each processed sample was weighed into a Tefon digestion tube.Subsequently, 4 mL of 65% nitric acid (HNO 3 ) and 2 mL of 30% hydrogen peroxide (H 2 O 2 ) were added.Te tubes were allowed to stand overnight to maximize digestion efciency.Te following day, the samples were processed in a MARS6 microwave oven at a temperature setting of 190 °C for a 30minute digestion cycle.Upon reaching room temperature, the digested solutions were diluted using deionized water up to a 50 mL volume in a volumetric fask and then fltered through an 11 μm flter paper before subsequent analytical procedures.

Results of the Spectral Signals and Elemental Composition of Sausage Samples. Figure 1 depicts the characteristic FT-IR spectrum of the sausage sample with peaks concentrated in
Journal of Analytical Methods in Chemistry the fngerprint region.When superimposed on the obtained spectra, there is almost no diference between samples of diferent brands.In consideration of the full spectra of all samples, it was mostly impossible to diferentiate the dissimilarities.Tus, peaks of the spectrum are selected to reduce unnecessary data.In which, the wavelength 3100-3700 cm −1 is the oscillation of the O-H functional group; the wavelength 2851-3007 cm −1 and 1380-1425 cm −1 arise from the C-H vibrations while the bands at 1537-1625 cm −1 correspond to the C�C vibrations.Te bands at 1023-1240 cm −1 result from the vibrations of group C-O.Since raw spectral data from FT-IR analysis are insufcient for the classifcation study, principle component analysis is the chosen multivariate statistical analysis to process the new data of selected peaks.
Te FT-IR spectrum, predominantly concentrated in the fngerprint region as depicted in Figure 1, initially indicated minimal variance between samples of diferent brands, posing a challenge in distinguishing them based purely on raw spectral data.Tis observation underscores the complexity of the sausage matrix and suggests that the subtle diferences in the composition of the sausages are not readily discernible in the fngerprint region of the FT-IR spectrum alone.Te selection of specifc peaks within the spectrum aimed at reducing data redundancy was a strategic approach.Te wavelengths ranging from 3100 to 3700 cm−1, 2851-3007 cm−1, 1380-1425 cm−1, and 1023-1240 cm−1, corresponding to the vibrations of various functional groups (O-H, C-H, C�C, and C-O), provide crucial insights into the molecular structure of the sausages.However, these wavelengths alone were not sufcient to diferentiate the brands efectively, indicating that the variances in the chemical composition of the sausages from diferent brands might be more nuanced and require a more refned analytical approach.
Te utilization of principal component analysis (PCA) in this context emerges as a vital tool.PCA's capability to transform the original variables into a new set of uncorrelated variables, thereby reducing data dimensionality and enhancing the elucidation of data structure, is particularly useful.Trough PCA, the study could reveal underlying patterns or trends in the spectral data that are indicative of brand-specifc characteristics.Tese characteristics could arise from various factors such as diferences in the quality and source of ingredients, processing techniques, and even the geographical origin of raw materials.In further discussions, it would be pertinent to delve into how these brand-specifc characteristics, unraveled by PCA,  Measured isotopic positions of elements 11 B, 23 Na, 24 Mg, 27 Al, 28 Si, 39 K, 43 Ca, 51 V, 52 Cr, 55 Mn, 63 Cu, 66 Zn, 69 Ga, 75 As, 85 Rb, 88 Sr, 107 Ag, 111 Cd, 121 Sb, 133 Cs, 137 Ba, 202 Hg, and 208 Pb 4 Journal of Analytical Methods in Chemistry could be linked to the particularities of each brand's production process, ingredient selection, and quality control measures.For instance, variations in the concentrations of certain elements such as sodium, potassium, or iron could be attributed to the use of diferent curing agents, spices, or meat types.Te implications of these fndings for future research are vast.Tey suggest that a combination of FT-IR spectroscopy and PCA, along with potentially other analytical techniques, could be employed more broadly in the food industry for quality control, authentication of origin, and even detection of adulteration.
In the detailed discussion of Table 2, which provides specifc quantitative metrics for both essential and toxic elements in sausage samples from six diferent brands, certain numerical values stand out, highlighting the variation in elemental composition across these brands.Each brand's sample, represented by 10 individual samples and subjected to triplicate measurements, ofers a robust statistical framework to analyze these elemental distributions.
Le Gourmet's samples, for instance, displayed remarkably low concentrations of elements such as aluminum (Al), chromium (Cr), manganese (Mn), iron (Fe), copper (Cu), and barium (Ba), with their levels falling below the instrument's limit of detection (LOD).Tis is particularly signifcant in the case of iron (Fe), an essential nutrient, where its insufcient presence in Le Gourmet sausages could raise questions about its nutritional adequacy.
In stark contrast, the Vissan brand demonstrated exceptionally high sodium (Na) levels, with an average concentration of 39,436.30± 4736.78 μg/g.Tis concentration is notably high compared to standard nutritional recommendations and could have health implications, especially for individuals with hypertension or those on sodiumrestricted diets.Such high sodium content in Vissan sausages underscores the importance of consumer awareness regarding dietary sodium intake.
Ebol brand sausages were characterized by their high magnesium (Mg) content, averaging 2,416.57μg/g.Tis contrasts sharply with the magnesium content in Le Gourmet sausages, which was only 446.03 μg/g-less than half of that found in the Butcher brand, the next lowest, with an average magnesium concentration of 1,045 μg/g.Tis signifcant diference in magnesium content among brands could be a refection of the varying ingredient profles or additives used.
Iron concentrations also varied considerably across brands.Vissan sausages contained a notably high iron concentration of 773.34 μg/g, while Le Gourmet's iron levels were so low they fell below the LOD.Tis disparity in iron content could be a crucial factor for consumers making dietary choices based on iron intake requirements.
Mercury (Hg), quantifed in μg/kg due to its minimal occurrence, was another element analyzed.Although the presence of mercury in food is a concern for food safety, the concentrations in all sausage samples were below the FDA's reporting limit [23].Tis fnding, while reassuring, emphasizes the need for ongoing vigilance in monitoring toxic elements in food products.
Tese specifc quantitative fndings from the study reveal a diverse elemental landscape across diferent sausage brands.Tey highlight the necessity for consumers to consider the elemental composition of sausages in their dietary choices, especially given the potential health implications of elements such as sodium and iron.For manufacturers, these results underscore the importance of ingredient selection and processing methods in infuencing the fnal product's elemental makeup, directly impacting the nutritional profle and safety of the sausages.

Data Analysis with Multivariate Analysis.
Principal component analysis (PCA) serves as an invaluable computational strategy in multivariate statistics, primarily designed to reduce the high dimensionality inherent to complex datasets.By transforming the original variables into a new set of uncorrelated variables, termed principal components, PCA facilitates the elucidation of the data structure, revealing underlying patterns or trends that might otherwise go undetected.
Within the realm of food science, PCA has proven itself as a robust analytical method capable of classifying food products based on a myriad of physicochemical attributes.Recent advancements have extended its application to the categorization of food items based on their metal element profles, serving as an indirect marker for geographical origin or processing techniques [30].For example, a pivotal study by Singh and Ghosh [31] employed PCA in the classifcation of various honey brands, discovering that regional variations signifcantly infuenced the metal content profles, thereby allowing for efective diferentiation [25].Another compelling case is presented by Xu et al., who utilized PCA to segregate Chinese green tea samples, demonstrating that region-specifc diferences in metal element profles could be clearly delineated using this approach [32].
Te analytical power of PCA lies not just in dimensionality reduction but also in its ability to identify key variables-here, specifc metal elements-that make substantial contributions to the variance within the data, thus becoming salient features for classifcation.For instance, in the context of quality and safety assessments of sausages, Ammor and Yaakoubi [33] leveraged spectral data in conjunction with PCA to diferentiate strains of lactic acid bacteria in fermented sausages.Furthermore, PCA provides the added beneft of generating biplots or scatter plots, ofering a visual representation that simplifes the interpretative process [32].
Considerable attention was devoted to the meticulous preprocessing and scaling of Fourier transform infrared spectroscopy (FTIR) spectral data for its incorporation into a principal component analysis (PCA) framework.Te procedural steps were consistently implemented across all sections of the research to ensure methodological coherence.Specifcally, the absorption peaks that were the focus of the multivariate analyses were carefully selected to correspond with distinct molecular vibrations relevant to the chemical composition of the samples under investigation.
Te spectral regions that were targeted for this analysis include the following: (i) Wavelengths ranging from 3100 to 3700 cm −1 and 1380 to 1425 cm −1 , which are predominantly indicative of the vibrational modes associated with hydroxyl (O-H) functional groups (ii) Spectral bands spanning the wavenumber intervals of 2851 to 3007 cm −1 emanate from the vibrations of the C-H bonds commonly found in organic compounds (iii) Absorption peaks were observed between 1537 and 1625 cm −1 , representing C�C vibrational modes (iv) Bands ranging from 1023 to 1240 cm −1 are associated with the C-O functional group vibrations.
Following the objectives and requirements of the study, no logarithmic transformations were applied to the spectral data.Te rationale behind this decision was to maintain methodological alignment across diferent sections of the study.Rather, a process of numerical conversion and scaling was meticulously executed to ensure that each variable contributed uniformly to the PCA model.For this purpose, the raw spectral data were processed using Te Unscrambler X software (CAMO, Oslo, Norway).Tis specialized software facilitated the transformation of the spectral data into a numerical matrix format conducive to subsequent multivariate statistical analyses.
In this study, Figure 2 shows the results of PCA performance on the FT-IR dataset of 6 sausage brands.It can be seen that the frst 2 PCs account for over 90% of the total sample variation.Terefore, it can be said that these PCs carry the most signifcant information of the dataset and the PCA visualization on the new coordination was reliable.Te separation of 6 sample groups corresponding to their brands can be seen on the PCA score plot.Notably, sausages from 4 brands of Vissan, ÐN Á, Le Gourmet, and Ebol were the most classifed samples due to their distinctive distributions on the PCA plot.Although the distribution of a few samples from Lacus and Le Gourmet nearly overlapped, in general, the sausages of these two brands are still distinguishable.On the other hand, it is noticeable that the spectral signals of the samples from Bucher and Lacus are indistinctive.Most of the samples of these two brands are overlapped and unseparated.Girardeau and Passot [34] used PCA to analyze the fuorescence spectra of lactic acid bacteria.Te results show similarities to this experiment's results as the discriminant map factors show certain factors are identifed while several appear overlapped.Te combination of the infrared spectroscopy dataset and the multivariate statistical method has shown the feasibility of classifying sausage brands.
Another dataset of chemical composition commonly used in food discrimination is the metal content [35,36].Te average metal content of 60 sausage samples was determined by the ICP-MS instrument (Table 2).Te average concentration of 20 elements was selected as the input data for the PCA analysis, employing STATISTICA software.Te results of the PCA analysis are presented in Figures 3(a) and 3(b).In the two-way point scatter plot based on PC1 and PC3 (Figure 3), the sausage samples from the 6 brands were separated.Tis highlighted the ability of the PCA method to distinguish the brand name origin of the sausage samples based on the variation of elemental composition.Additionally, the degree of variables' (elemental) contribution to the separation of sample classes and the correlation among variables is depicted in the loading scatterplot (Figure 3(b)).
Tere are 6 variables that play the principal role in the separation of each class, including Cu, Cr, Mg, Zn, Cd, and Hg.Notably, the frst four elements are positively correlated and carry the highest weight in the classifcation of the frst PC.Meanwhile, although Cd and Hg are also the major contributors to the distribution of 6 sample classes on PC2, they display a negative correlation due to their opposite values nearly 1 and -1 on PC2, respectively.Te moving range diagrams illustrate the means and the common distributions of the variables in the cases.Te Ebol sample had a much higher concentration of Mg, Cr, and Cu than the rest of the samples, which can be used as a distinguishing mark from other brands (Figure 4(a)).Meanwhile, Vissan models had signifcantly higher Ti content than other brands.Te combination of Ca and Cd factors was identifed as the main distinguishing factor for sausages produced by Bucher.Te combination of K and Zn factors also contributed to the pattern diferentiation of Lacus.As for the Le Gourmet sample, no elemental isotopes were identifed with high concentrations; however, it can be distinguished based on the Hg content which is nearly twice as high as that of the Bucher and Vissan samples.Similarly, it was difcult to determine the factors that distinguish sausages from the ÐN Á brand, except that the Hg content was slightly higher than that of the other brands.
Multivariate statistics serves as an indispensable tool in the realm of complex data analysis, particularly when dealing with multidimensional variables that require simultaneous examination to extract meaningful patterns or trends.Te advantage of multivariate methods such as principal component analysis (PCA) or cluster analysis is their ability to distill multiple variables into essential factors, thereby aiding in more incisive interpretation and decisionmaking.
However, the size of the data set introduces its own set of challenges that cannot be overlooked.Large and complex data sets demand considerable computational power and memory resources, which can be a limiting factor especially if the analyses are being run on standard computing devices.Tis computational burden not only afects the speed but can also infuence the accuracy and reliability of the results, especially when computational shortcuts or approximations are employed to manage large data sets.
Terefore, preparatory measures are often required to enable efcient and accurate analyses.Training in advanced computational methods and statistical software can ofer researchers the skills necessary to optimize data analysis procedures.For instance, knowledge of high-performance computing practices can enable the execution of analyses that would otherwise be computationally prohibitive.
Additionally, the use of secondary algorithms aimed at variable reduction can be invaluable.In contexts like spectral analysis, where hundreds or even thousands of variables might be collected for each sample, algorithms can be employed to eliminate redundant or irrelevant variables, thus reducing the dimensionality of the data.Tis simplifcation not only eases the computational burden but also helps in avoiding overftting, thereby improving the model's predictive accuracy.Te use of powerful computing devices equipped with high-speed processors and ample memory can substantially mitigate the challenges posed by large data sets.In some cases, cloud-based computing solutions or parallel processing techniques can be employed to distribute the computational load across multiple devices or servers, making it feasible to analyze extremely large or complex data sets.
In the multivariate analysis, the application of PCA in this research provides a quintessential example of its utility in handling high-dimensional and complex datasets.Te PCA methodology successfully transformed the spectral and elemental data into a set of principal components, ofering a more insightful interpretation of the data.Tis approach has revealed subtle but signifcant diferences in the chemical profles of the six sausage brands, which were not immediately apparent in the raw data.Te PCA's ability to distill these nuances is particularly evident in the diferentiation of the brands based on their metal element profles.Te specifc elements, including Cu, Cr, Mg, Zn, Cd, and Hg, emerged as key diferentiators among the brands.Tis highlights PCA's    capability in not just reducing the dimensionality of the dataset but also in pinpointing specifc variables that are critical in distinguishing between the sausage brands.Te correlation observed among elements, as well as their varying concentrations in diferent brands, suggests a complex interplay of factors that could be infuenced by the brand's source of ingredients, processing methods, and quality control protocols.For instance, the signifcantly higher concentrations of Mg, Cr, and Cu in Ebol samples, compared to other brands, could be indicative of specifc processing practices or ingredient sources unique to Ebol.Similarly, the high Ti content in Vissan and the distinct combination of Ca and Cd in Bucher sausages ofer a unique fngerprint of these brands.Such elemental disparities provide valuable insights into the potential health implications of these products, especially considering elements such as sodium and mercury, which have direct relevance to consumer health.Tis study's fndings underscore the complexity of food matrices like sausages and the challenges in their analysis.Te successful application of PCA in this context demonstrates the method's potential in food science research, particularly for brand diferentiation and quality control.It also suggests avenues for future research, such as exploring the underlying reasons behind these elemental variations and their implications for food safety and nutrition.However, the analysis also brings to light the computational challenges inherent in handling large datasets.Te need for powerful computing resources and sophisticated statistical software is evident.Tis requirement underscores the importance of investing in advanced computational infrastructure and training for researchers to efectively manage and interpret complex datasets.Such capabilities are essential for harnessing the full potential of multivariate statistical methods like PCA, ensuring not only the efciency of the analysis but also the accuracy and reliability of the fndings.
In summary, this research, through its innovative use of PCA in conjunction with FT-IR and ICP-MS analyses, ofers a novel approach to food product diferentiation and quality assessment.Te study contributes signifcantly to the feld of food science, providing a template for future research in food product authentication and safety evaluation.It also highlights the need for continued advancements in computational methods and resources to keep pace with the increasing complexity of food science research.

Conclusion
Trough the FT-IR method, the study demonstrated the feasibility of using infrared spectroscopy to classify and distinguish between diferent sausage brands.Tis not bolsters FT-IR spectroscopy as a promising tool for food diferentiation but also emphasizes its sensitivity to the variations in the composition of such products.Results from ICP-MS provided a clear distinction between sausage brands based on their elemental composition.Notably, elements such as K, Ca, Ti, Ba, and Ni were pivotal in driving these distinctions.Tis sheds light on the importance of considering elemental compositions when characterizing and classifying food products.
Tis study underscored the efectiveness of combined analytical methodologies in diferentiating commercially produced sausages.By integrating FT-IR spectroscopy and ICP-MS metal analysis, a robust platform for distinguishing between sausage brands based on compositional nuances was developed.Specifcally, the infrared spectroscopy indicated potential in food diferentiation due to its sensitivity to composition variations.Concurrently, the elemental composition results from ICP-MS, emphasizing the role of elements such as K, Ca, Ti, Ba, and Ni, distinctly classifed sausage brands.Trough PCA's application to both datasets, the research illuminated the complementary nature of these sources in food product classifcation.Ultimately, our fndings highlight a promising avenue for enhancing food product characterization, a critical step in ensuring food safety, authenticity, and quality.

Figure 1 :
Figure 1: Main peaks of FT-IR spectrum of sausage samples.

Figure 2 :
Figure 2: Scree plot and PCA visualization of the sausage dataset obtained by FT-IR.

Table 1 :
Operating parameters of ICP-MS.